Direct numerical simulation of turbulent channel flow over a surrogate for Nikuradse-type roughness

M Thakkar,A Busse,N D Sandham

doi:10.1017/jfm.2017.873

Abstract

A tiled approach to rough surface simulation is used to explore the full range of roughness Reynolds numbers, from the limiting case of hydrodynamic smoothness up to fully rough conditions. The surface is based on a scan of a standard grit-blasted comparator, subsequently low-pass filtered and made spatially periodic. High roughness Reynolds numbers are obtained by increasing the friction Reynolds number of the direct numerical simulations, whereas low roughness Reynolds numbers are obtained by scaling the surface down and tiling to maintain a constant domain size. In both cases, computational requirements on box size, resolution in wall units and resolution per minimum wavelength of the rough surface are maintained. The resulting roughness function behaviour replicates to good accuracy the experiments of Nikuradse (1933 VDI-Forschungsheft, vol. 361), suggesting that the processed grit-blasted surface can serve as a surrogate for his sand-grain roughness, the precise structure of which is undocumented. The present simulations also document a monotonic departure from hydrodynamic smooth-wall results, which is fitted with a geometric relation, the exponent of which is found to be inconsistent with both the Colebrook formula and an earlier theoretical argument based on low-Reynolds-number drag relations.

Highlights

IntroductionThe equivalent sand-grain roughness height, ks, was first defined by Schlichting (1936) as the size of the sand grains from the experiments of Nikuradse (1933) that gave effectively the same frictional resistance as the roughness under consideration
The behaviour of an irregular realistic grit-blasted surface, in the entire Reynolds number range from the transitionally rough to the fully rough regime, has been studied using direct numerical simulation (DNS), with a tiling approach employed to simulate cases with low roughness Reynolds number, which presents a different set of challenges to cases with high Reynolds number
The simulations identify theoretical issues relating to the approach to hydrodynamic smoothness, since neither the Colebrook curve nor Bradshaw’s quadratic law is close to the DNS results

Summary

Introduction

The equivalent sand-grain roughness height, ks, was first defined by Schlichting (1936) as the size of the sand grains from the experiments of Nikuradse (1933) that gave effectively the same frictional resistance as the roughness under consideration.

Objectives

Results

Conclusion